Question

A thrown ball's path can be modeled by the equation h(t) = -16t2 + 8t +5, where h is the height in feet. How long before the ball hit the ground?

a. 0.86 seconds
b. 1.28 seconds
c. -1.27 seconds
d. 0 seconds

Answer 1

To find when the ball hits the ground, solve for t when h(t) is 0 in the equation h(t) = -16t^2 + 8t + 5. Using the quadratic formula, t is about 1.28 seconds, which is option b.

Step-by-step explanation:

To determine how long before the ball hits the ground, we need to find when the height h(t) is equal to zero in the equation h(t) = -16t2 + 8t + 5. We can solve for t when h(t) = 0 using the quadratic formula:

t = (-b ± √(b2 - 4ac)) / (2a)

Here, a = -16, b = 8, and c = 5 from our equation, yielding two potential solutions for t. However, since we are looking for a time after the ball has been thrown, we disregard the negative solution and only consider positive time values.

Using the quadratic formula, we find that t is approximately 1.28 seconds when the ball hits the ground. Therefore, the answer is b. 1.28 seconds.